The Tynecastle Park club negotiated a sell-on agreement with Bologna when the full-back was sold in the summer of 2020, understood to be more than ten per cent.
The 20-year-old has agreed a five-year deal and will travel to England to undergo a medical this week.
After featuring for Bologna 12 times in his first season, Hickey was a first-team regular for Siniša Mihajlović, playing 36 times in Serie A and scoring five goals.
His form attracted the attention of AC Milan as well as a number of Premier League clubs, including Arsenal. Now Brentford have won the race for his signature and he will link up with former Celtic defender Kristoffer Ajer.
In turn, Hearts will get a significant windfall to be added to the income they will generate from at least eight games in Europe this season.
“There definitely is a sell-on," Hearts sporting director Joe Savage told the Evening News in May. “There are a lot of rumours but we need to see if they will come true or not and whether Aaron is actually going to sign for another club
“Any club in the world developing and selling players, you have to protect yourself,” he said.
“You want a sell-on in the deal, you want some sort of add-ons in it or a buy-back option. Whatever it may be, you need to look after the interests of your own club. Hearts did that with Aaron.”